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Thread: Functions

  1. #1
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    Exclamation Functions

    Question:
    Find $\displaystyle \frac{f(x+h)-f(x)}{h} $ where h is not equal to zero and $\displaystyle f(x)=\sqrt{x} $.

    Attempt:
    $\displaystyle = \frac{\sqrt{x+h}-\sqrt{x}}{h} $
    I have to rationalize the numrator
    $\displaystyle = \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x}} $

    Now how to simplify?

    Thank you
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  2. #2
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    Quote Originally Posted by mj.alawami View Post
    Question:
    Find $\displaystyle \frac{f(x+h)-f(x)}{h} $ where h is not equal to zero and $\displaystyle f(x)=\sqrt{x} $.

    Attempt:
    $\displaystyle = \frac{\sqrt{x+h}-\sqrt{x}}{h} $
    I have to rationalize the numrator
    $\displaystyle = \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x})} $

    Now how to simplify?

    Thank you
    $\displaystyle \frac{(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x}}{h(\sqrt{x+h}+\sqrt{ x})}=\frac{1}{(\sqrt{x+h}+\sqrt{x})} $
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